正特征中多个zeta值的塔库尔基猜想

IF 4.6 Q2 MATERIALS SCIENCE, BIOMATERIALS ACS Applied Bio Materials Pub Date : 2023-01-01 DOI:10.1017/fmp.2023.26

Chieh-Yu Chang, Yen-Tsung Chen, Yoshinori Mishiba

{"title":"正特征中多个zeta值的塔库尔基猜想","authors":"Chieh-Yu Chang, Yen-Tsung Chen, Yoshinori Mishiba","doi":"10.1017/fmp.2023.26","DOIUrl":null,"url":null,"abstract":"Abstract In this paper, we study multiple zeta values (abbreviated as MZV’s) over function fields in positive characteristic. Our main result is to prove Thakur’s basis conjecture, which plays the analogue of Hoffman’s basis conjecture for real MZV’s. As a consequence, we derive Todd’s dimension conjecture, which is the analogue of Zagier’s dimension conjecture for classical real MZV’s.","PeriodicalId":2,"journal":{"name":"ACS Applied Bio Materials","volume":null,"pages":null},"PeriodicalIF":4.6000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"On Thakur’s basis conjecture for multiple zeta values in positive characteristic\",\"authors\":\"Chieh-Yu Chang, Yen-Tsung Chen, Yoshinori Mishiba\",\"doi\":\"10.1017/fmp.2023.26\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract In this paper, we study multiple zeta values (abbreviated as MZV’s) over function fields in positive characteristic. Our main result is to prove Thakur’s basis conjecture, which plays the analogue of Hoffman’s basis conjecture for real MZV’s. As a consequence, we derive Todd’s dimension conjecture, which is the analogue of Zagier’s dimension conjecture for classical real MZV’s.\",\"PeriodicalId\":2,\"journal\":{\"name\":\"ACS Applied Bio Materials\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.6000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACS Applied Bio Materials\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1017/fmp.2023.26\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATERIALS SCIENCE, BIOMATERIALS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Bio Materials","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1017/fmp.2023.26","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","Score":null,"Total":0}

引用次数: 3

摘要

摘要本文研究了正特征函数域上的多个zeta值(简称MZV)。我们的主要成果是证明了Thakur的基猜想，它对实MZV起着类似Hoffman基猜想的作用。因此，我们导出了Todd的维数猜想，它是经典实MZV的Zagier维数猜想的类比。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

On Thakur’s basis conjecture for multiple zeta values in positive characteristic

Abstract In this paper, we study multiple zeta values (abbreviated as MZV’s) over function fields in positive characteristic. Our main result is to prove Thakur’s basis conjecture, which plays the analogue of Hoffman’s basis conjecture for real MZV’s. As a consequence, we derive Todd’s dimension conjecture, which is the analogue of Zagier’s dimension conjecture for classical real MZV’s.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

ACS Applied Bio Materials Chemistry-Chemistry (all)

CiteScore

9.40

自引率

2.10%

发文量

464